Question

Let . Show that$\mathit{A}\mathit{L}{\mathit{L}}_{\mathbf{\text{DFA}}}$is decidable.

Short answer

It can be shown that $AL{L}_{\text{DFA}}$is decidable.

Step-by-step solution

Explain decidability

The automata and the grammars helps decide the outcome of the undecidable problems. The Deterministic Finite Automata determines the state of the string given as input.

Show that ALLDFA is decidable

Consider the given context-free language, . Assume that the following Turing Machine $M$decides $AL{L}_{\text{DFA}}$.

1. Construct $DFA E$recognizes the complete situation, the start state $A$, until new states are marked by the transition, if no accept state is marked “accept”, otherwise, “reject”.
2. Run the Turing Machine $T$, on input , where$T$ decides $E_{\text{DFA}}$.
3. If$T$ accepts, “accept”.
4. If$T$ rejects, “reject”.

Therefore, the $AL{L}_{\text{DFA}}$is decidable.